The paper introduces an asynchronous value‑iteration RL algorithm for average‑reward multichain MDPs that requires only the transition graph and uses Bather’s decomposition to partition the state space into communicating subsystems and transient states. This hierarchical decomposition transforms the global decision problem into structured subproblems, enabling the algorithm to converge to the optimal gain and produce gain‑optimal policies in finite time. Two additional algorithms are presented: one that approximately solves the multichain average optimality equations for near gain‑optimality, and another that approximates the optimal bias function to achieve near bias‑optimality, both with almost‑sure convergence guarantees and improved transient performance. whyItMatters":"The work offers the first essentially model‑free average‑reward RL algorithms for general multichain MDPs, avoiding reductions to discounted problems."
arXiv:2606. 16729v1 Announce Type: new Abstract: While there is an extensive body of work characterizing the sample complexity of discounted cumulative-reward MDPs, finite sample analyses for average-reward MDPs have been limited, and most existing works rely on restrictive assumptions such as ergodicity or access to a generative model.
arXiv:2603. 23461v2 Announce Type: replace Abstract: We study reinforcement learning (RL) with linear function approximation in Markov Decision Processes (MDPs) satisfying \emph{linear Bellman completeness} -- a fundamental setting where the Bellman backup of any linear value function remains linear.
The paper introduces a framework for reinforcement learning in Markov decision processes where policies are ordered by the information they provide, allowing data from one policy to estimate the performance of others. An epoch‑based algorithm is developed for infinite‑horizon average‑cost MDPs with continuous state and action spaces, achieving regret that scales with the width of the policy class’s information order. The authors apply the framework to lost‑sales inventory, dual‑sourcing, and state‑dependent queueing systems, demonstrating improved regret bounds and empirical performance without requiring global convexity or specific arrival‑rate structures.
The paper introduces a framework for optimal policy improvement in reinforcement learning, defining it as the best single update under given constraints. It shows that restricting improvement to a subset of states is equivalent to solving an induced Markov Decision Process, linking planning with explicit or implicit models to optimal policy improvement. The authors develop a novel operator for greedification under approximate evaluation, demonstrating empirical gains across several RL algorithms and settings.
arXiv:2512. 14617v2 Announce Type: replace-cross Abstract: Many practical decision-making problems involve tasks whose success depends on the entire system history, rather than on achieving a state with desired properties.
We study infinite-horizon average-reward constrained Markov decision processes (CMDPs) under the weakly communicating assumption. Existing high-probability guarantees for this setting either require c...
arXiv:2609.00504v1 Announce Type: cross Abstract: In this work, we study radically uncoupled learning in discounted general-sum Markov games. Assuming ``$\mathsf{ETH}$ for $\mathsf{PPAD}$", we show t...
arXiv:2607. 17823v1 Announce Type: new Abstract: Reinforcement Learning is a cornerstone technique for modern large reasoning models.
The paper introduces a computationally efficient algorithm for infinite-horizon average-reward constrained Markov decision processes (CMDPs) under weak communication. It achieves a high-probability regret and cumulative constraint violation of ×O(√T) in the tabular setting, matching optimal dependence up to logarithmic factors. The method augments the state with cumulative constraint violation, reshapes rewards using a Huber potential, and applies finite-horizon approximation with optimistic value iteration to maintain bounded per-step rewards.
arXiv:2511. 19849v2 Announce Type: replace-cross Abstract: Recurrence objectives, where a target region must be visited infinitely often, are a fundamental class of specifications for Markov decision processes (MDPs) and form the core of $\omega$-regular and linear temporal logic (LTL) objectives.
arXiv:2606. 00367v1 Announce Type: cross Abstract: Reinforcement learning problems typically define the goal as maximizing the expected value of a scalar reward function.
arXiv:2606. 17377v1 Announce Type: new Abstract: We study performance-driven environment abstraction for decision-making in large Markov decision processes.